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Sun Systems makes two models of retractable awnings – Standard (hand cranked) and Premium (motorized). The profit per unit sold is $250 (for Standard models) and $600 (for Premium models). Each Standard unit of requires 20 minutes of machine assembly time and Premium unit requires 50 minutes of machine assembly time. The machine used for assembly has 30 hours of processing time available during the week. Because of the manufacturing process employed for every 4 units of the Standard model produced at least 1 unit of the Premium model must be produced. a) Formulate the problem of determining how many units of each model to produce in a week as a linear programming problem. Show objective function and all constraints. Determine how many of each model should be produced in a week to maximize profit.